Is there a name for word combination structures that embed other words within them (both verbal or written)? (Any less rude example would be appreciated.)
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Wikipedia’s definition of a “deliberate mondegreen” matches your example. As Bob says, this is a double entendre. A deliberate mondegreen is a sub-species of double entendre that exploits homophony to get across its second meaning.
This is called a double entendre, wherein a spoken phrase is devised to be understood in more than one way. You’d typically call something like “sofa king” a gag name, a false name meant to elicit humor either through some sort of double entendre or pun.
In many cases (such as your own), it’s a rather vulgar type of humor. For example, it was popular in the naming of “Bond girls” in James Bond films:
Even spoofs like the Austin Powers movies caught on with names like Alotta Fagina in Austin Powers: International Man of Mystery.
These are puns. They are a specific kind of pun, but I don't believe there is a special word for that kind of pun alone.
The British satirical magazine Private Eye runs letters with assumed names that can be read as words, and that section is titled Pseudo Names.